Empirical Isochrones and the R-C gap

Firstly in Mayne et
al (2007) we present many photometric catalogues which we make
freely available. To aid navigation we present a table of all the
photometry available here.

Secondly a version with high resolution figures (as an alternative to
the one on astro-ph) is available here.

In
Mayne et al (2007) we create empirical isochrones by selecting
members from a collection of OB associations, clusters, groups and
sub-groups (all termed clusters from hereon). Then we fit a cubic
spline through these members using a median binning procedure to
follow the sequence locus. Once we have created the empirical
isochrones we compare the sequences on a relative age plot. To do this
we must adjust the sequences to absolute magnitude and colour, using
distances and extinctions taken from the literature. For the
parameters (distance and extinction) we use those derived using
methods as free from PMS isochrone fitting as is possible in each
case, as we are attempting to compare PMS ages. Once the sequences are
adjusted a selection of sequences are taken as fiducial clusters,
these are objects which generally have oft confirmed ages (within the
literature) or accurate independent of PMS isochrone ages. To best
apply relative ages for each cluster the fiducials must be chosen to
adequately sample the CMD space. Using this method we have been able
to generate an age sequence for our selected clusters which is as
follows. The youngest groups can be collated into three sets of
similar ages. The youngest set is the ONC, NGC6530 and IC5146
(nominally 1 Myrs); next Cep OB3b, NGC2362, λ Ori and NGC2264
(nominally 3 Myrs); and finally σ Ori and IC348 (nominally 4-5
Myrs). With the older groups the relative ages are much less robust,
however they are ordered thus: NGC7160 (~10Myrs), h and χ Per
(~13Myrs), NGC1960 (~16Myrs) and NGC2547 (~35Myrs).

The empirical isochrones and relative age studies of Mayne et al (2007) give two key insights into
stellar chronology and secular evolution. First, when comparing the
sequences in absolute colour and magnitude it became clear that the
largest source of uncertainty is often the distances to the
clusters. A typical uncertainty in distance modulus to a young cluster
is ~0.2, although this is often exceeded. For instance the ONC has a
distance modulus estimate of 8.38+/-0.37, a difference of
approximately 0.4 in V0. The second insight is a feature we
term the R-C gap, which is displayed in the figure at the top in the
left panel for the ONC. This feature is a separation between the fully
convective PMS stars gravitationally contracting along almost vertical
Hayashi tracks and radiative stars on the MS. This feature has been
noted before in the literature, but it's underlying physics and
potential uses have not been highlighted e.g
Stolte et al (2004) call this the PMS/MS transition region (they
identified it in a Js, Js-Ks CMD of
NGC3603). To understand the physics behind the R-C gap we refer to the
figure on the right in the top panel. This figure shows mass tracks
from
Siess and Dufour (2000) for stars of 7, 6, 5, 4, 3, 2, 1.2, 1.0,
and 0.8 Solar masses (dashed lines) and isochrones of 0.1, 1, 3 and 13
Myrs (solid lines). The red line indicates the transition in CMD space
of 1 and 3 solar mass stars between 1 and 3Myrs. As can be seen from
the mass tracks as a star forms a radiative core and travels along a
Henyey track towards the MS it moves a relatively large distance in
CMD space when compared to a star still gravitationally
contracting. This is partly due to the temperature of the star
increasing whilst the size remains almost constant but is exacerbated
by the nature of a CMD i.e. the scale is very much smaller on the x
axis as a CMD is a y vs y-x format. The particular importance of the
R-C gap however is its dependence on age and independence from
distance. The size of the dislocation between the PMS and MS stars
changes with age, as a cluster ages the stars joining the MS are of
decreasing mass and their transition point is closer to the existing
MS isochrone. For a young cluster only the massive stars will be on
the MS and these will evolve to it very quickly leaving a large
dislocation. Irrespective of the cluster distance the gap size can be
used as an age indicator. The evolution of the gap can be seen through
the clusters in the figure below, first as a dislocation in the ONC
(~1Myr) and in NGC2264 (~3Myrs) then as a terminus to the PMS in
σ Orionis (~4Myrs) and finally as a small dislocation between the
MS and PMS in h and χ Per.